Tomographic reconstruction with non-linear diagonal estimators

In tomographic reconstruction, the inversion of the Radon transform in the presence of noise is numerically unstable. Reconstruction estimators are studied where the regularization is performed by a thresholding in a wavelet or wavelet packet decomposition. These estimators are efficient and their optimality can be established when the decomposition provides a near-diagonalization of the inverse Radon transform operator and a compact representation of the object to be recovered. Several new estimators are investigated in different decomposition. First numerical results already exhibit a strong metrical and perceptual improvement over current reconstruction methods. These estimators are implemented with fast non-iterative algorithms, and are expected to outperform Filtered Back-Projection and iterative procedures for PET, SPECT and X-ray CT devices

Regularization in tomographic reconstruction using thresholding estimators

In tomographic medical devices such as SPECT or PET cameras, image reconstruction is an unstable inverse problem, due to the presence of additive noise. A new family of regularization methods for reconstruction, based on a thresholding procedure in wavelet and wavelet packet decompositions, is studied. This approach is based on the fact that the decompositions provide a near-diagonalization of the inverse Radon transform and of the prior information on medical images. An optimal wavelet packet decomposition is adaptively chosen for the specific image to be restored. Corresponding algorithms have been developed for both 2-D and full 3-D reconstruction. These procedures are fast, non-iterative, flexible, and their performance outperforms Filtered Back-Projection and iterative procedures such as OS-EM

De-noising SPECT/PET Images Using Cross-Scale Regularization

De-noising of SPECT and PET images is a challenging task due to the inherent low signal-to-noise ratio of acquired data. Wavelet based multi-scale denoising methods typically apply thresholding operators on sub-band coefficients to eliminate noise components in spatial-frequency space prior to reconstruction. In the case of high noise levels, detailed scales of sub-band images are usually dominated by noise which cannot be easily removed using traditional thresholding schemes. To address this issue, a cross-scale regularization scheme is introduced, which takes into account cross-scale coherence of structured signals. Preliminary results show promising performance in denoising clinical SPECT and PET images for liver and brain studies. Wavelet thresholding was also compared to denoising with a brushlet expansion. The proposed regularization scheme eliminates the need for threshold parameter settings, making the denoising process less tedious and suitable for clinical practice

The anomalous Hall effect in non-collinear antiferromagnetic Mn3_{3}NiN thin films

We have studied the anomalous Hall effect (AHE) in strained thin films of the frustrated antiferromagnet Mn$_{3}$NiN. The AHE does not follow the conventional relationships with magnetization or longitudinal conductivity and is enhanced relative to that expected from the magnetization in the antiferromagnetic state below $T_{\mathrm{N}} = 260$\,K. This enhancement is consistent with origins from the non-collinear antiferromagnetic structure, as the latter is closely related to that found in Mn$_{3}$Ir and Mn$_{3}$Pt where a large AHE is induced by the Berry curvature. As the Berry phase induced AHE should scale with spin-orbit coupling, yet larger AHE may be found in other members of the chemically flexible Mn$_{3}A$N structure

Regularization in Tomographic Reconstruction Using Thresholding Estimators

In tomographic medical devices such as single photon emission computed tomography or positron emission tomography cameras, image reconstruction is an unstable inverse problem, due to the presence of additive noise. A new family of regularization methods for reconstruction, based on a thresholding procedure in wavelet and wavelet packet (WP) decompositions, is studied. This approach is based on the fact that the decompositions provide a near-diagonalization of the inverse Radon transform and of prior information in medical images. A WP decomposition is adaptively chosen for the specific image to be restored. Corresponding algorithms have been developed for both two-dimensional and full three-dimensional reconstruction. These procedures are fast, noniterative, and flexible. Numerical results suggest that they outperform filtered back-projection and iterative procedures such as ordered-subset-expectation-maximization

Analysis of the Temporal Organization of Sleep Spindles in the Human Sleep EEG Using a Phenomenological Modeling Approach

The sleep electroencephalogram (EEG) is characterized by typical oscillatory patterns such as sleep spindles and slow waves. Recently, we proposed a method to detect and analyze these patterns using linear autoregressive models for short (≈ 1 s) data segments. We analyzed the temporal organization of sleep spindles and discuss to what extent the observed interevent intervals correspond to properties of stationary stochastic processes and whether additional slow processes, such as slow oscillations, have to be assumed. We have found evidence for such an additional slow process, most pronounced in sleep stage 2

High resolution synchrotron imaging of wheat root hairs growing in soil and image based modelling of phosphate uptake

Root hairs are known to be highly important for uptake of sparingly soluble nutrients, particularly in nutrient deficient soils. Development of increasingly sophisticated mathematical models has allowed uptake characteristics to be quantified. However, modelling has been constrained by a lack of methods for imaging live root hairs growing in real soils.We developed a plant growth protocol and used Synchrotron Radiation X-ray Tomographic Microscopy (SRXTM) to uncover the 3D interactions of root hairs in real soil. We developed a model of phosphate uptake by root hairs based directly on the geometry of hairs and associated soil pores as revealed by imaging.Previous modelling studies found that root hairs dominate phosphate uptake. By contrast, our study suggests that hairs and roots contribute equally. We show that uptake by hairs is more localised than by roots and strongly dependent on root hair and aggregate orientation.The ability to image hair-soil interactions enables a step change in modelling approaches, allowing a more realistic treatment of processes at the scale of individual root hairs in soil pores